We present and discuss the Klein-Gordon and Dirac wave equations in the de Sitter universe. To obtain the Dirac wave equation we use the factorization of the second-order invariant Casimir operator associated to the Fantappie-de Sitter group. Both the Klein-Gordon and Dirac wave equations are discussed in terms of the spherical harmonics with spin weight. A particular case of Dirac wave equation is solved in terms of a new dass of polynomials.382585598